Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x + 1$ and $ JT = 9x - 1$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x + 1} = {9x - 1}$ Solve for $x$ $ -2x = -2$ $ x = 1$ Substitute $1$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({1}) + 1$ $ JT = 9({1}) - 1$ $ CJ = 7 + 1$ $ JT = 9 - 1$ $ CJ = 8$ $ JT = 8$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {8} + {8}$ $ CT = 16$